CN104573846B - A kind of polymorphism job shop layout optimization method based on CA PSO hybrid optimization algorithms - Google Patents
A kind of polymorphism job shop layout optimization method based on CA PSO hybrid optimization algorithms Download PDFInfo
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Abstract
A kind of polymorphism job shop layout optimization method based on CA PSO hybrid optimization algorithms, comprises the following steps：1) build the machine cellular in workshop, additionally arrange cellular, passage cellular and spacing cellular, 2) coding of the particle based on 2N dimensional vectors, 3) primary is produced by SLP methods, 4) the constraint penalty functional value of particle is calculated, 5) fitness value of particle is calculated, 6) iterations t, accelerator coefficient c are set1、c2, inertia coeffeicent w, 7) and cellular updates the state of oneself by tracking fitness value, and each particle is optimized according to evolution formula, finally gives optimal particle.Shop logistics can effectively be reduced by plant layout's scheme obtained by this method and carry total cost.
Description
Technical field
The present invention relates to one kind is based on cellular machine (Cellular Automata, hereinafter referred to as CA) and improves population calculation
The polymorphism job shop layout of the hybrid optimization algorithm of method (Particle Swarm Optimization, hereinafter referred to as PSO)
Optimization method, belongs to industrial engineering and areas of information technology.
Background technology
With increasingly fierce, the large-scale foundry under a class complex product Mass Customization Enterprises and industry cluster of market competition
Enterprise, its production process increasingly highlights the various of form and state on the levels such as order, equipment, technique, batch and bottleneck
Property, flexibility, robustness and the dynamic demand of layout progressively strengthen, and such Workshop layout new problem is referred to as " polymorphism
Job shop is laid out ".
At present applied to plant layout study intelligent optimization algorithm have genetic algorithm (GA), simulated annealing (SA),
Tabu search algorithm (TS) etc., but when applying to solve polymorphism job shop location problem by these algorithms, exist
The problem of slow computationally intensive, convergence, low efficiency, optimizing scarce capacity.
The content of the invention
It is of the invention to propose that one kind is based on to overcome the shortcomings of that prior art is solving the layout presence of polymorphism job shop
The polymorphism job shop layout optimization method of CA-PSO hybrid optimization algorithms, makes it when solving polymorphism job shop layout
Optimal equipment arrangement can be sought, so as to obtain the optimization method more adapted to than existing layout method.
The technical solution adopted for the present invention to solve the technical problems is：
A kind of polymorphism job shop layout optimization method based on CA-PSO hybrid optimization algorithms, the optimization method bag
Include following steps：
1. a kind of polymorphism job shop layout optimization method based on CA-PSO hybrid optimization algorithms, it is characterised in that：
The layout optimization method is comprised the steps of：
(1) cellular automata model of polymorphism job shop layout is set up.To workshop, (L × W, L are workshop length, and W is workshop
Width) among machine, auxiliary equipment, passage, the spacing of machinery compartment carry out abstract, set up machine cellular, additionally arrange cellular, it is logical
Road cellular and spacing cellular are as follows：
The status attribute of machine cellular t is expressed as：
In formula：
mp--- machine cellular position (i, j) within a grid；
mn--- the title of machine；
mi--- the spacing required for machine arrangement；
ml--- machine length；
mw--- machine-wide；
ms--- machine arrangement states, ms∈ { 0,1 }, 0 represents laterally to put, and 1 represents that longitudinal direction is put.
The status attribute for additionally arranging cellular t is expressed as：
In formula：
ap--- additionally arrange cellular position (i, j) within a grid；
an--- the title of auxiliary equipment；
ai--- the spacing required for auxiliary equipment arrangement；
al--- auxiliary equipment length；
aw--- auxiliary equipment width；
as--- auxiliary equipment arrangement states, as∈ { 0,1 }, 0 represents laterally to put, and 1 represents that longitudinal direction is put.Passage cellular t
The status attribute at moment is expressed as：
In formula：
ps--- passage cellular position (i, j) within a grid；
pm--- main channel size；
ps--- subchannel size；
pa--- passage cellular attribute, pa∈ { 0,1 }, 0 represents main channel, and 1 represents subchannel.
The status attribute of spacing cellular t is expressed as：
In formula：
Ss--- spacing cellular position (i, j) within a grid；
Sf--- spacing cellular is in grid (i+1, j) direction spacing, Sf∈{al,aw,pm,ps}；
Sb--- spacing cellular is in grid (i-1, j) direction spacing, Sf∈{al,aw,pm,ps}；
Sl--- spacing cellular is in the spacing in grid (i, j+1) direction, Sf∈{al,aw,pm,ps}；
Sr--- spacing cellular is in the spacing in grid (i, j-1) direction, Sf∈{al,aw,pm,ps}。
(2) encode.Assuming that plant layout's cellular automata model have N number of cellular (including machine cellular, additionally arrange cellular, passage member
Born of the same parents and spacing cellular), each layout candidate scheme is expressed as a particle, then the coding of each particle be 2N dimension to
Amount：
P=(x1,x2,…,xN, y1,y2,…,yN) (5)
In formula, preceding N-dimensional represents the x coordinate of each cellular, and rear N-dimensional represents the y-coordinate of each cellular.
The heading and speed of each particle are also the vector of a 2N dimension：
V=(vx1,vx2,…,vxN, yx1,yx2,…,yxN) (6)
In formula, preceding N-dimensional represents the translational speed in the x directions of each cellular, and rear N-dimensional represents the shifting in the y directions of each cellular
Dynamic speed.
(3) primary is produced.The cellular to be arranged to workshop is by using SLP methods (System Layout
Planning, Systematic layout planning) analysis calculating is carried out, preliminary placement scheme is obtained, primary is used as.
(4) the constraint penalty value of particle is calculated according to formula (7).
In formula, δ1、δ2For penalty coefficient；If penalty value is 0, the particle meets constraints.
(5) fitness value of particle is calculated according to formula (8).
In formula, Q={ 1,2 ..., q } represents the part type set processed in the production of units cycle of workshop；Represent
The material trucking expenses of part q production processes per unit distance between cellular n and cellular m；Represent part q production processes
Material carries frequency between cellular n and cellular m；DnmRepresent the distance between cellular n and cellular m.
(6) iterations t, accelerator coefficient c are set1、c2, inertia coeffeicent w.
Iterations t as the optimization method end condition；Accelerator coefficient c1、c2It is most important parameter in PSO algorithms
One of.It reflect particle in searching process by individual and global information effect, it to balance flight particle part
Search capability and ability of searching optimum play vital effect.The setting of accelerator coefficient can produce difference in varied situations
As a result, set for a certain particular problem；Inertia coeffeicent w is also one of most important parameter in PSO algorithms, it big
The small new speed for determining particle flight inherits the inertial system that linear decrease is used in the degree retained, the present invention to original speed
Number, by constantly reducing the gradient information that original speed is included, to reduce influence of the local extremum at optimization initial stage to algorithm.
(7) optimize.In optimization process, cellular updates the state of oneself by tracking fitness value, each particle
Line translation is entered in position by formula (9)~formula (12), and fitness value is compared, and picks out wherein optimal particle, i.e., optimal
Plant layout's scheme.
Vxi(t+1)=wVxi(t)+c1·rand()·[pxi(t)-xi(t)]+c2·rand()·[pxg(t)-xi
(t)]
I=1,2 ..., N； (9)
Vyi(t+1)=wVyi(t)+c1·rand()·[pyi(t)-yi(t)]+c2·rand()·[pyg(t)-yi
(t)]
I=1,2 ..., N； (10)
xi(t+1)=xi(t)+Vxi(t+1) i=1,2 ... N； (11)
yi(t+1)=yi(t)+Vyi(t+1) i=1,2 ... N； (12)
In formula (9)~formula (12)：
T --- iterations；
c1、c2--- accelerator coefficient；
Rand () --- it is evenly distributed on the random number between (0,1)；
W --- inertia coeffeicent；
pxi--- the desired positions in the x directions of i-th of cellular experience；
pyi--- the desired positions in the y directions of i-th of cellular experience；
pxg--- the desired positions in the x directions that all cellulars are lived through；
pyg--- the desired positions in the y directions that all cellulars are lived through.
The technical concept of the present invention：Because polymorphism job shop various resources to be arranged are various, and workshop geometry
Constraints, logistics relation and functional relationship are complicated, therefore require higher to the intelligent optimization algorithm of plant layout, it is desirable to can
Large-scale location problem is solved, on the premise of ensuring that there is no solution precocity and being absorbed in locally optimal solution, can rapidly be sought
Find globally optimal solution.
The present invention exactly solves the problems, such as polymorphism job shop using the powerful computing capability of CA-PSO algorithms.Cellular machine
A time and space all discrete dynamical systems, the discrete space being made up of the cellular of limited state, with it is synchronous more
New the characteristics of；Particle cluster algorithm is a unconfined optimized algorithm, with the ability efficiently calculated.CA-PSO algorithms are thought
Think：By cellular machine come each resource cellular of abstract structure polymorphism job shop, then by particle cluster algorithm seek it is global most
Excellent solution, in searching process, each resource cellular state synchronized updates.
The substantial effect of the present invention is embodied in：1.CA-PSO optimized algorithms have fast convergence rate, it is easier to tend to global
The characteristics of optimal solution；2. car can effectively be reduced based on the polymorphism job shop placement scheme obtained by CA-PSO optimized algorithms
Between logistics cost, improve floor space utilization rate.
Brief description of the drawings
Fig. 1 is polymorphism job shop cellular automata model figure
Fig. 2 schemes for plant layout of the embodiment of the present invention
Embodiment
With reference to the accompanying drawings and examples, present disclosure is illustrated.
Certain automobile tail pipe workshop area is 35m × 30m, and resource to be arranged has wire cutting machine, punch press etc. to be shown in Table 1 institute
Show；The logistics capacity of each machinery compartment is shown in Table 2.The minimum spacing m of machinei=0.9m；The minimum spacing a additionally arrangedi=0.8m；Each equipment
Between material carry use trolley, carry unit price be 1.5 × 10-4Member/rice × part.
The size and number of the equipment of table 1
Equipment room logistics capacity (the unit of table 2：Part)
1) build machine cellular 45, additionally arrange cellular 11, passage cellular 30 and spacing cellular 56.
The status attribute of machine cellular t is expressed as：
In formula：
mp--- machine cellular position (i, j) within a grid；
mn--- the title of machine；
mi--- the spacing required for machine arrangement；
ml--- machine length；
mw--- machine-wide；
ms--- machine arrangement states, (ms∈ { 0,1 }), 0 represents laterally to put, and 1 represents that longitudinal direction is put.
The status attribute for additionally arranging cellular t is expressed as：
In formula：
ap--- additionally arrange cellular position (i, j) within a grid；
an--- the title of auxiliary equipment；
ai--- the spacing required for auxiliary equipment arrangement；
al--- auxiliary equipment length；
aw--- auxiliary equipment width；
as--- auxiliary equipment arrangement states, (as∈ { 0,1 }), 0 represents laterally to put, and 1 represents that longitudinal direction is put.
The status attribute of passage cellular t is expressed as
In formula：
ps--- passage cellular position (i, j) within a grid；
pm--- main channel size；
ps--- subchannel size；
pa--- passage cellular attribute, (pa∈ { 0,1 }), 0 represents main channel, and 1 represents subchannel.
The status attribute of spacing cellular t is expressed as：
In formula：
Ss--- spacing cellular position (i, j) within a grid；
Sf--- spacing cellular is in grid (i+1, j) direction spacing, Sf∈{al,aw,pm,ps}；
Sb--- spacing cellular is in grid (i-1, j) direction spacing, Sf∈{al,aw,pm,ps}；
Sl--- spacing cellular is in the spacing in grid (i, j+1) direction, Sf∈{al,aw,pm,ps}；
Sr--- spacing cellular is in the spacing in grid (i, j-1) direction, Sf∈{al,aw,pm,ps}。
2) encode.Plant layout's cellular automata model has 142 cellulars, and each layout candidate scheme is expressed as a grain
Son, then the coding of each particle is the vector of one 284 dimension：
P=(x1,x2,…,x142, y1,y2,…,y142) (5)
In formula, preceding 142 dimension table shows the x coordinate of each cellular, and rear 142 dimension table shows the y-coordinate of each cellular.
The heading and speed of each particle are also the vector of one 284 dimension：
V=(vx1,vx2,…,vx142, yx1,yx2,…,yx142) (6)
In formula, preceding 142 dimension table shows the translational speed in the x directions of each cellular, and rear 142 dimension table shows the y directions of each cellular
Translational speed.
3) primary is produced.The cellular to be arranged to workshop is by using SLP methods (System Layout
Planning, Systematic layout planning) analysis calculating is carried out, preliminary placement scheme is obtained, primary is used as.
4) the constraint penalty functional value of particle is calculated according to formula (7).
Take penalty coefficient δ1、δ2For 0.5.
5) fitness value of particle is calculated according to formula (8).
In formula, Q={ 1,2 ..., q } represents the part type set processed in the production of units cycle of workshop；Represent
The material trucking expenses of part q production processes per unit distance between cellular n and cellular m；Represent part q production processes
Material carries frequency between cellular n and cellular m；DnmRepresent the distance between cellular n and cellular m.
6) iterations t=100, accelerator coefficient c are set1=1.2, c2=1.2, inertia coeffeicent w=0.5.
7) optimize.In optimization process, cellular updates the state of oneself, the position of each particle by tracking fitness value
Put and enter line translation by formula (9)~formula (12), fitness value is compared, wherein optimal particle is picked out.
Vxi(t+1)=wVxi(t)+c1·rand()·[pxi(t)-xi(t)]+c2·rand()·[pxg(t)-xi
(t)]
I=1,2 ..., N； (9)
Vyi(t+1)=wVyi(t)+c1·rand()·[pyi(t)-yi(t)]+c2·rand()·[pyg(t)-yi
(t)]
I=1,2 ..., N； (10)
xi(t+1)=xi(t)+Vxi(t+1) i=1,2 ... N； (11)
yi(t+1)=yi(t)+Vyi(t+1) i=1,2 ... N； (12)
In formula (9)~formula (12)：
T --- iterations；
c1、c2--- accelerator coefficient；
Rand () --- it is evenly distributed on the random number between (0,1)；
W --- inertia coeffeicent；
pxi--- the desired positions in the x directions of i-th of cellular experience；
pyi--- the desired positions in the y directions of i-th of cellular experience；
pxg--- the desired positions in the x directions that all cellulars are lived through；
pyg--- the desired positions in the y directions that all cellulars are lived through.
After above-mentioned specific implementation step, the present embodiment plant layout figure is as shown in Fig. 2 calculate obtained total logistics cost
For 9860000 yuan, and this workshop does not use 1250000 yuan of total logistics cost before this layout optimization method.For treating arrangement money
The various polymorphism job shop in source, logistics total cost can be substantially reduced using the placement scheme obtained by the inventive method.
Content described in this specification embodiment is only enumerating to the way of realization of inventive concept, protection of the invention
Scope is not construed as being only limitted to the concrete form that embodiment is stated, protection scope of the present invention is also and in art technology
Personnel according to present inventive concept it is conceivable that equivalent technologies mean.
Claims (1)
1. a kind of polymorphism job shop layout optimization method based on CA-PSO hybrid optimization algorithms, it is characterised in that：It is described
Layout optimization method is comprised the steps of：
(1) cellular automata model of polymorphism job shop layout is set up；To the machine among workshop, auxiliary equipment, passage, machine
Between spacing carry out abstract, plant size is L × W, and L is workshop length, and W is workshop width, sets up machine cellular, additionally arranges member
Born of the same parents, passage cellular and spacing cellular are as follows：
The status attribute of machine cellular t is expressed as：
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In formula：
mp--- machine cellular position (i, j) within a grid；
mn--- the title of machine；
mi--- the spacing required for machine arrangement；
ml--- machine length；
mw--- machine-wide；
ms--- machine arrangement states, ms∈ { 0,1 }, 0 represents laterally to put, and 1 represents that longitudinal direction is put；
The status attribute for additionally arranging cellular t is expressed as：
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<mi>t</mi>
</msubsup>
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<mi>a</mi>
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<mo>,</mo>
<msub>
<mi>a</mi>
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<mo>,</mo>
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<mi>a</mi>
<mi>i</mi>
</msub>
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<mi>a</mi>
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<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：
ap--- additionally arrange cellular position (i, j) within a grid；
an--- the title of auxiliary equipment；
ai--- the spacing required for auxiliary equipment arrangement；
al--- auxiliary equipment length；
aw--- auxiliary equipment width；
as--- auxiliary equipment arrangement states, as∈ { 0,1 }, 0 represents laterally to put, and 1 represents that longitudinal direction is put；
The status attribute of passage cellular t is expressed as：
<mrow>
<msubsup>
<mi>S</mi>
<mrow>
<mi>p</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
</mrow>
<mi>t</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>p</mi>
<mi>s</mi>
</msub>
<mo>,</mo>
<msub>
<mi>p</mi>
<mi>m</mi>
</msub>
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<mi>p</mi>
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<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：
ps--- passage cellular position (i, j) within a grid；
pm--- main channel size；
ps--- subchannel size；
pa--- passage cellular attribute, pa∈ { 0,1 }, 0 represents main channel, and 1 represents subchannel；
The status attribute of spacing cellular t is expressed as：
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<msubsup>
<mi>S</mi>
<mrow>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
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<mi>j</mi>
<mo>)</mo>
</mrow>
</mrow>
<mi>t</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mi>s</mi>
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<mo>,</mo>
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<mi>S</mi>
<mi>f</mi>
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<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：
Ss--- spacing cellular position (i, j) within a grid；
Sf--- spacing cellular is in grid (i+1, j) direction spacing, Sf∈{al,aw,pm,ps}；
Sb--- spacing cellular is in grid (i-1, j) direction spacing, Sf∈{al,aw,pm,ps}；
Sl--- spacing cellular is in the spacing in grid (i, j+1) direction, Sf∈{al,aw,pm,ps}；
Sr--- spacing cellular is in the spacing in grid (i, j-1) direction, Sf∈{al,aw,pm,ps}；
(2) encode；Assuming that plant layout's cellular automata model has N number of cellular, including machine cellular, additionally arrange cellular, passage cellular and
Each layout candidate scheme, is expressed as a particle by spacing cellular, then the coding of each particle is the vector of a 2N dimension：
P=(x1,x2,…,xN, y1,y2,…,yN) (5)
In formula, preceding N-dimensional represents the x coordinate of each cellular, and rear N-dimensional represents the y-coordinate of each cellular；
The heading and speed of each particle are also the vector of a 2N dimension：
V=(vx1,vx2,…,vxN, yx1,yx2,…,yxN) (6)
In formula, preceding N-dimensional represents the translational speed in the x directions of each cellular, and rear N-dimensional represents the mobile speed in the y directions of each cellular
Degree；
(3) primary is produced；The cellular to be arranged to workshop carries out analysis calculating by using SLP methods, obtains preliminary cloth
Office's scheme, is used as primary；
(4) the constraint penalty value of particle is calculated according to formula (7)；
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<mi>w</mi>
</msub>
<mo>+</mo>
<msub>
<mi>m</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<msub>
<mi>a</mi>
<mi>s</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
</mrow>
</munder>
<mrow>
<mo>(</mo>
<msub>
<mi>a</mi>
<mi>w</mi>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, δ1、δ2For penalty coefficient；If penalty value is 0, the particle meets constraints；
(5) fitness value of particle is calculated according to formula (8)；
<mrow>
<mi>F</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>q</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>Q</mi>
</msubsup>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</msubsup>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</msubsup>
<msubsup>
<mi>P</mi>
<mrow>
<mi>n</mi>
<mi>m</mi>
</mrow>
<mi>q</mi>
</msubsup>
<msubsup>
<mi>F</mi>
<mrow>
<mi>n</mi>
<mi>m</mi>
</mrow>
<mi>q</mi>
</msubsup>
<msub>
<mi>D</mi>
<mrow>
<mi>n</mi>
<mi>m</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, Q={ 1,2 ..., q } represents the part type set processed in the production of units cycle of workshop；Represent part q
The material trucking expenses of production process per unit distance between cellular n and cellular m；Represent part q production processes in cellular
Material carries frequency between n and cellular m；DnmRepresent the distance between cellular n and cellular m；
(6) iterations t, accelerator coefficient c are set1、c2, inertia coeffeicent w；
(7) optimize；In optimization process, cellular updates the state of oneself, the position of each particle by tracking fitness value
Enter line translation by formula (9)~formula (12), fitness value is compared, wherein optimal particle, i.e., optimal workshop is picked out
Placement scheme；
Vxi(t+1)=wVxi(t)+c1·rand()·[pxi(t)-xi(t)]+c2·rand()·[pxg(t)-xi(t)] i=
1,2…,N； (9)
Vyi(t+1)=wVyi(t)+c1·rand()·[pyi(t)-yi(t)]+c2·rand()·[pyg(t)-yi(t)] i=
1,2,…,N； (10)
xi(t+1)=xi(t)+Vxi(t+1) i=1,2 ... N； (11)
yi(t+1)=yi(t)+Vyi(t+1) i=1,2 ... N； (12)
In formula (9)~formula (12)：
T --- iterations；
c1、c2--- accelerator coefficient；
Rand () --- it is evenly distributed on the random number between (0,1)；
W --- inertia coeffeicent；
pxi--- the desired positions in the x directions of i-th of cellular experience；
pyi--- the desired positions in the y directions of i-th of cellular experience；
pxg--- the desired positions in the x directions that all cellulars are lived through；
pyg--- the desired positions in the y directions that all cellulars are lived through.
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